In this article we review the present knowledge on the elastic properties of membranes of biological origin. Assuming the fluid mosaic hypothesis, we consider the phospholipid bilayer as the structural base of a biological membrane. We expose a model due to Helfrich which can be used to obtain an expression for the membrane elastic energy. The free energy is completely characterized by two local principal curvatures and four parameters that depend on the chemical composition of the membrane and its local environment. In addition we present the theoretical justification of an experimental method (the Micropipette Manipulation technique) that may be used to measure the membrane rigidity (the elastic constant that corresponds to the mean curvature of the membrane). Finally, we describe some physical consequences of these concepts, such as the explanation of the lamellarsponge phase transition and the emergence of the steric interaction between membranes.